MOFM-Nav: On-Manifold Ordering-Flexible Multi-Robot Navigation

2025-10-20

AI Summary

Maintaining flexible spatial ordering among multiple robots navigating along an m-dimensional implicit manifold (m ≥ 2) in n-dimensional Euclidean space remains challenging due to topological constraints and non-Euclidean metric distortions. Method: This paper proposes a distributed cooperative control framework based on Coordinated Gradient Virtual Fields (CGVF). By introducing decoupled auxiliary vectors and a virtual coordinate mechanism, the approach eliminates topologically invariant singularities and ensures global convergence under non-Euclidean metrics. Implicit function zero-level-set modeling, combined with dynamic neighbor communication, enables adaptive ordering and reconfigurable formation control. Results: Simulations demonstrate strong robustness, adaptability, and fault tolerance—particularly under high-dimensional manifolds, arbitrary initial configurations, and single-robot failures. The method significantly enhances flexibility and scalability of multi-robot coordinated navigation on implicit manifolds.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Multiagent Systems: Coordination and Collaboration
• Machine Learning: Learning with Manifolds

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

This paper addresses the problem of multi-robot navigation where robots maneuver on a desired (m)-dimensional (i.e., (m)-D) manifold in the $n$-dimensional Euclidean space, and maintain a {it flexible spatial ordering}. We consider $ mgeq 2$, and the multi-robot coordination is achieved via non-Euclidean metrics. However, since the $m$-D manifold can be characterized by the zero-level sets of $n$ implicit functions, the last $m$ entries of the GVF propagation term become {it strongly coupled} with the partial derivatives of these functions if the auxiliary vectors are not appropriately chosen. These couplings not only influence the on-manifold maneuvering of robots, but also pose significant challenges to the further design of the ordering-flexible coordination via non-Euclidean metrics. To tackle this issue, we first identify a feasible solution of auxiliary vectors such that the last $m$ entries of the propagation term are effectively decoupled to be the same constant. Then, we redesign the coordinated GVF (CGVF) algorithm to {it boost} the advantages of singularities elimination and global convergence by treating $m$ manifold parameters as additional $m$ virtual coordinates. Furthermore, we enable the on-manifold ordering-flexible motion coordination by allowing each robot to share $m$ virtual coordinates with its time-varying neighbors and a virtual target robot, which {it circumvents} the possible complex calculation if Euclidean metrics were used instead. Finally, we showcase the proposed algorithm's flexibility, adaptability, and robustness through extensive simulations with different initial positions, higher-dimensional manifolds, and robot breakdown, respectively.

Problem

• Multi-robot navigation on m-dimensional manifolds in Euclidean space
• Maintaining flexible spatial ordering using non-Euclidean metrics
• Decoupling strongly coupled propagation terms for manifold maneuvering

Innovation

• Decouples propagation terms using auxiliary vectors
• Redesigns GVF algorithm with virtual coordinates
• Enables flexible coordination via shared virtual coordinates